Study of Photoexcited States and Nonlinear Optical Responses in Insulating Copper Oxides

莫特绝缘体中的电荷隙是由强电子相关引起的。因此，我们期望光学响应与带绝缘体中的光学响应不同。在。本项目采用半填充Hubbard模型及其有效模型，从理论上研究了典型Mott绝缘体中绝缘铜氧化物的光激发态和非线性光学响应，并应用数值精确对角化技术对有效模型进行了研究。我们发现，与自旋和电荷分离的一维相比，系统中光掺杂载流子和局域自旋的相互作用在非线性光学响应中起着至关重要的作用。我们还发现，二维绝缘铜的双磁子拉曼散射的异常入射光子能量依赖是由自旋的存在引起的。为了阐明光激发态对维数的依赖性，我们研究了线性光吸收光谱的温度依赖性。在一维体系中，由于自旋-电荷分离，在低温下不存在明显的温度依赖性。相反，在二维中发现了特征温度依赖，这来自载流子和自旋的相互作用。非线性光学响应不仅有光学允许态的影响，也有禁止态的影响。为了检查这两种状态的分布，我们执行了动态密度矩阵重整化群计算。一维哈伯德模型。我们发现在实际材料中，大库仑相互作用下的态的简并性被提升了。

Charge gap in the Mott insulator originates from strong electron correlation. Therefore, we expect optical responses that are different from those in the band insulator. In. this project, we theoretically examine photoexcitaed states and nonlinear optical responses in insulating copper oxides that are typical Mott insulators by using a half filled Hubbard model and its effective modelWe investigated the nonlinear optical responses in the two-dimensional Mott insulator, applying the numerically exact diagonalization technique to the effective model. We found that, in contrast to one dimension where spin and charge are separated, the interplay of photo-doped carriers and localized spins in the system plays a crucial role in the nonlinear optical responses. We also found that anomalous incident-photon energy dependence of the two-magonon Raman scattering in two-dimensional insulating cuprates is caused by the presence of the spins. In order to clarify the dependence of photoexcited states on dimensionality, we examined the temperature dependence of the linear optical absorption spectrum. In one-dimensional system, the there is no remarkable temperature dependence at low temperature because of spin-charge separation. In contrast, characteristic temperature dependences are found in two dimensions, which come from the interplay of carriers and spins. Not only the optically allowed but also forbidden states contributes in the nonlinear optical responses. To examine the distribution of both the states, we performed a dynamical density-matrix renormalization group calculation for the. one-dimensional Hubbard model. We found that the degeneracy of the states seen at large Coulomb interaction is lifted in real materials.